mrn-1 – cell dimensioning - intranet deibhome.deib.polimi.it/capone/wn/mrn-en-1-cell...
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Politecnico di MilanoFacoltà di Ingegneria dell’Informazione
MRN-1 – Cell dimensioning
Mobile Radio NetworksProf. Antonio Capone
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Cell radius
o How can we calculate the coverage radius of a radio base station?
o It should be quite easy, given:n PT = transmitted power (dBm)n Pth = receiver threshold (dBm) – receiver sensibilityn LP=PT - Pth maximum path loss
o We calculate the radius from the formula of LP as a function of the distance:n Propagation factor h:
n or using Okumura-Hata model
÷÷ø
öççè
æ×=
010log10)(dddLP h
A. Capone: Mobile Radio Networks 2
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Exampleo Given:
n Received power at 10 m = 100 mWn Receiver threshold: Pth= -50 dBmn h = 3.7
o We get:
mR
RR
PdRdPRP
mPdP
thdBmRdBmR
dBmRdBmR
7801010
3770
10log50
10log3720
log10)()(
20)100(log10)10()(
3770
1010
010][0][
10][][0
=×=®
=÷øö
çèæ®-=÷
øö
çèæ-
=÷÷ø
öççè
æ-=
===
h
The outage probability at cell edge is however in this case 50%! Why?
A. Capone: Mobile Radio Networks 3
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Fading margin
o The example does not consider the shadowing that causes deviations from the value estimated by propagation models based on distance
o It is possible to consider shadowing reducing the cell radius for taking a safety margin on the variations of received power
o Fading marginn M = power at cell edge (dBm) –
receiver threshold (dBm)
Average path loss M
Pdf of path loss
LP=PT - Pth
LP=PT - Pth - M
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Example (continuation)o Given:
n Received power at 10 m = 100 mWn Receiver threshold: Pth= -50 dBmn h = 3.7n Log-normal shadowing with sdB=4dBn Fading margin M=6 dB
o We get:
mRR
MPdRdPRP thdBmRdBmR
537101065010
log3720
log10)()(
3764
10
010][0][
=×=®+-=÷øö
çèæ-
+=÷÷ø
öççè
æ-= h
A. Capone: Mobile Radio Networks 5
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Outage probabilityo Since shadowing has a log-normal distribution which in
dB is Gaussian, we have:
fPdB (r ) (x) = 12π ⋅σ dB
e− x−PdB (r )( )2 /2σ dB2
PdB (r) = power at distance r, PdB (r) = ave. value
Outage is experienced when power < Pth (dB):
÷÷ø
öççè
æ -== ò
¥- dB
thdBP
rPoutPrPerfcdxxfr
th
dB s2)(
21)()(Pr )(
A. Capone: Mobile Radio Networks 6
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Outage probabilityo Re-writing power as a function of its value at cell edge (R)
we get:
PdB (r) = PdB (R)−10η log10rR
o And then:
÷÷ø
öççè
æ -=
=÷÷ø
öççè
æ --=
dB
dB
thdBout
RrMerfc
RrPRPerfcr
sh
sh
2/log10
21
2/log10)(
21)(Pr
10
10
÷÷ø
öççè
æ=
dBout
MerfcRs22
1)(Pr
o Obviously at cell edge:
A. Capone: Mobile Radio Networks 7
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Example (continuation)
o Then: Prout(R)=6.68%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
400 500 600 700
r
Out
age
prob
abili
ty
■ PdB(10 m)= 20 dBm■ Pth= -50 dBm■ h = 3.7■ sdB=4dB■ M=6 dB■ R=537 m
Remind that: ϕ(x) = 12
1+ erf x2
!
"#
$
%&
'
()
*
+,, where ϕ(x) is the CDF of the normal distribution
and then: erfc(x) = 2 1−ϕ x 2( )'(
*+
A. Capone: Mobile Radio Networks 8
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Outage areao To calculate the outage area in a circular area
of radius R we just need to integrate:
ò
ò
ò
ò
÷ø
öçè
æ -=
=÷÷ø
öççè
æ -=
=÷÷ø
öççè
æ -=
==
1
0
1
0
10
0
10
02
2ln)ln(
2log10
2/log10
2)(Pr1)(Pr
dxxmerfcx
dxxMerfcx
RdrRrMerfc
Rr
drrrR
R
dB
R
dB
R
outAout
sh
sh
sh
pp
[ ][ ]ï
ïî
ïïí
ì
==
=
mWPmWRPm
th
M
dB
)(10
10
10ln
10/
ss
A. Capone: Mobile Radio Networks 9
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Outage area
o Let us define:
( )
( ) ( )
( ) ( )212
1
)(22
)2(
)(22
1
0 21
2212
1
12212
1
12
21
21
21
21
ln)(Pr
QQerfceQerfc
erfceQerfce
derfceQ
dxQxQerfcxR
QQQ
Q
QQQQQ
Q
Aout
+-=
=úûù
êëé ---=
==
=÷÷ø
öççè
æ-=
-
¥-+
¥+-ò
ò
q
q
hs
s2
2)ln(
21 == QmQ
changing variable θ =Q1 −ln(x)Q2
A. Capone: Mobile Radio Networks 10
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Outage area
■ It represents the fraction of area “not covered”
■ h = 4■ Example.
■ s=6■ Target 1%è M=10
A. Capone: Mobile Radio Networks 11
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Outage at cell edge
■ h = 4■ Es.
■ s=6■ Target 1%è M=14
A. Capone: Mobile Radio Networks 12
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Computing cell radiuso Step 1
n From target outage probabilityn At cell edgen Or on the whole area
n And from values of sn We compute margin M
o Step 2n From receiver threshold Pth , propagation factor hn and transmitted power (or the power at a reference
distance)n We calculate radius R
A. Capone: Mobile Radio Networks 13
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Computing cell radius
kmRR
MPdRdPRP thdBmRdBmR
217.4101001070100
log405
log10)()(
4065
10
010][0][
=×=®+-=÷øö
çèæ-
+=÷÷ø
öççè
æ-= h
o Examplen s = 6 dBn h = 4n Prout(R) £ 0.01Þ M = 10n PR(100 m) = 5 dBmn Pth= -70 dBm
A. Capone: Mobile Radio Networks 14
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Fast and slow fading
Pth Pth+M1 Pth+M1+M2
1-2%
1-2%
M1 = slow fading margin
M2 = fast fading margin
A. Capone: Mobile Radio Networks 15
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Transmission over radio channel
A. Capone: Mobile Radio Networks 16
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Transmission over radio channel
■ WARNING: very brief discussion
See Wireless Communication course
See alsoH. Walke: “Mobile Radio Networks”, chapter 2. Section 7
A. Capone: Mobile Radio Networks 17
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Transmission over radio channelo When signal-to-noise ratio (SNR) is small it is possible to
improve the Bit Error Rate (BER) using forward error correction (FEC) codes
BPSKNo coding
10-1
10-6
Bit ErrorRate
Eb/No (dB)11 dB4 dB
A. Capone: Mobile Radio Networks 18
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Transmission over radio channel
o Correction codes allow to correct wrong bits adding redundant bits in the transmitted flow
o If out of n bits transmitted k are of information and (n-k) are redundancy, we define code rate the ratio k/n
A. Capone: Mobile Radio Networks 19
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Transmission over radio channel
o FEC codes improve BER performance
Rate 1/2
Uncoded BPSK
10-1
10-6
Bit ErrorRate
Eb/No (dB)
11 dB4 dB
Rate 3/4
A. Capone: Mobile Radio Networks 20
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Transmission over radio channel
o Code types:n Block codes
o Hammingo BCHo Reed-Solomon
n Continuous codeso Convolutionalo Turbo
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Transmission over radio channel
o Codes can be also used for revealing errors without being able to correct them
o When for instance we detect errors in a segment of coded voice it is possible to delete the segment and interpolate voice signal using correct samples
o When the type of service and the system allow (usually for data services) it is also possible to using retransmission techniques (ARQ –Automatic repeat ReQuest)
A. Capone: Mobile Radio Networks 22
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Transmission over radio channel
o In cellular systems the presence of high interference and high signal power fluctuations due to propagation pushed for the use of FEC codes with relatively small rates
o The use of FEC codes allows to reduce the minimum value of Signal-to-Noise and Interference Ration SIRmin tolerated by transmissions
o But at the cost of additional redundancy in the bit flow (the use of a ½ rate code halves the available capacity)
o Information theory demonstrates that channel capacity can be reached only using codes, however mobile radio channel is time varying and general conclusions cannot be easily drawn
A. Capone: Mobile Radio Networks 23
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Transmission over radio channelo Coding performance actually depends on the error statisticso Ideal BER curves of FEC codes assume white Gaussian
noise with independent errors (memoryless channel)o The radio channel in cellular systems tends to generate
correlated errors (memory channel) due to time varying characteristics of the channel and fluctuations of signal and interferences
Received power
t
Many errors
Few errors
A. Capone: Mobile Radio Networks 24
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Transmission over radio channelo The efficiency of most codes quickly decreases with
correlated errorso Therefore some mechanisms for shuffling transmitted bits
after coding are often used (bit interleaving)
Time
Am
plitu
de
Original Data Samples1 2 3 4 5 6 7 8 9
Interleaving Matrix
1 2 34 5 67 8 9
Transmitter
Interleaved Data Samples1 4 7 2 5 8 3 6 9
RF Transmission Path
Interleaved Data Samples1 4 7 2 5 8 3 6 9
Errors Clustered
De-Interleaving
Matrix
1 2 34 5 67 8 9
De-Interleaved Data Samples
1 2 3 4 5 6 7 8 9
Receiver
Errors DistributedA. Capone: Mobile Radio Networks 25
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Delay spreado Propagation over multiple paths can cause also other more
complex problems in case of digital transmissiono Different delays of signal replicas reaching the receiver
(delay spread) enlarge in time the impulse response of the channel and can generate inter-symbol interference (ISI)
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Delay spread
o The impact of the delay spread can be evaluated calculating its root mean square value (RMS Delay Spread):
( ) 2
1
2
1
1d
n
iiin
ii
RMS PP
ttt åå =
=
-=
( )
å
å
=
== n
ii
n
iii
d
P
P
1
1t
t
with■ tRMS RMS delay spread■ ti ritardo del path i■ Pi potenza ricevuta path i■ n numero di path
A. Capone: Mobile Radio Networks 27
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Delay spreado The inverse of the delay spread provides the coherence
bandwidtho If the coherence bandwidth is much larger than the signal
bandwidth than the delay spread has no impact on the reception
o If the coherence bandwidth is comparable or smaller than that of the signal, delay spread generates inter-symbol interference with degradation of reception
o In this case to overcome the frequency distortion of the channel we need to equalize it with a proper filter at reception
o Equalization techniques are usually based on channel estimation on known symbol sequences (see GSM), but can also be blind
o Other approaches are based on multi-carrier transmission
A. Capone: Mobile Radio Networks 28
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Voice coding
A. Capone: Mobile Radio Networks 29
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Voice coding: Time/Frequency characteristics
vocalized
Banda
See audio and video signal processing course
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Voice coding: Codecs
o Waveform codecs
o Source codecs (vocoders)
o Hybrid codecs
Analog-to-digital converters for voice
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Voice coding: Waveform codecs
o No ‘a priori’ information on the generated signal
o Required information: n Signal bandwidth B (classic telephony < 4 KHz)n Maximum quantization noise tolerable
samplerA to Db bits
Per sample
00100001
High quality, low complexity, low delay (one sample) Robustness to errors and background noise
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Voice coding: Pulse Code Modulation (PCM)
o standardized by ITU in 1960: G.711
o B=4 kHz, sampling frequency Bc=8 kHz, 8 bit/sample, 64 kb/s
o Two different quantization rules (logarithmic) n America (µ-law) n Europe (A-law) n With standard conversion rules
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Voice coding: Differential PCM (DPCM)
o Voice samples are correlated
o It is possible using prediction methods to estimate successive sample known previous ones
o And transmitting only the difference between predicted value and the real one
o Due to correlation the variance of the difference is smaller and require fewer bits for coding
predictor
+sampler +-
quant.
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Voice coding: Adaptive DPCM (ADPCM)
o Performance improves if predictor and quantization are adaptive
o Standardized in 1980 by ITU ADPCM at 32 kbit/s: G.721
o Later versions of ADPCM at 40, 32, 24, 16 kbit/s: G.726 e G.727
Adaptive predictor
+sampler +- Adaptive
Quantiz.
Low quality
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Voice coding: Sub Band Coding (SBC)
o Voice signal divided into sub-bands with filterso Signal of each sub-band is coded with techniques like
ADPCMo The advantage is that it is possible to use less bits for
the bands in witch human ear is less sensitive (more quantization noise is tolerable)
o Good quality:16-32 kbit/s higher complexity and delay
filtri codec
Es. G.722audio 7 kHz48,56, 64 kb/s
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Voice coding: Source codecs (vocoders)
o Based on human voice generation models
o Models allows to remove redundancy up to the basic information necessary for reproducing voice
o High complexityo Delay quite higho Sensitive to errors, background noise
and non-human sounds
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Voice coding: Model of human voice (phoneme)
o Reverberant filter with discrete parameterso Input signal (impulse sequence or white noise) o Parameters of the filter varying periodically (10-
20 ms)
pitch
Filter parameters Cn
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Voice coding: Linear vocoder (LPC)
Linear vocoders use the discrete parameters model with linear filterAt regular intervals (10-20 ms) model parameters are estimated and
transmittedn filter coefficients ai , n voiced/unvoiced flag, variance, pitch
å=
-=p
ii insans
1)(')(ˆ
A(z)
Sgain
Sintetic voiceEccitazione(20 ms)
Parameters estimation is based on error variance)()(ˆ)( nsnsne -=
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Voice coding: Linear Vocoder (LPC)
o Decoder uses received parameters for synthetizing a filter and reproducing voice
o High delay: segmentation, analysis, synthesis
o Quality: intelligible but not ‘natural’ (model limitations + problems with background noise)
o Low bit rate: < 2.4 kbit/s
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Voice coding: Input signals
o Classical input LPC with two states (es. LPC-10)o gain, pitch, flag voice/unvoiced
o Mixed inputo Both periodic input and pseudo random used simultaneously o 2 synthesis filters (low freq. » periodic input, high freq. »
pseudo random input)
o Residual inputo Ideal input signal: e(n)o Low bit rate coding of e(n)o It is no longer a real vocoder … towards hybrid codecs
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Voice coding: Hybrid codecs
o Hybrid codecs fill the gap between vocoders and waveform codecs
o More popular use the same approach of linear vocoder (LPC), but they optimize some parameters like the input signal (using the error signal)
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Voice coding: Hybrid codecs
o Multipulse-Excited Linear Prediction (MPLP), 1982
n Non uniform pulses with different amplitudes
n Position and amplitude of each pulse are determined based on an iterative procedure that minimizes error function
n ex. MPLP 9.6 kbit/s of BT for Skyphone service
o Regular Pulse Excitation (RPE)
n Regular pulse sequencen parameters: position of first pulse and periodn ex. LPT-RPE GSM 13 kbit/s
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Voice coding: Hybrid codecs
o Code Excited Linear Prediction (CELP)
n The input sequence is selected from a set of precoded sequences (code-book)
n Sequences in the code-book are instances of Gaussian processes
n Main problem: long delay due to the search procedure of the optimal sequence in the code book
n Algorithm semplification with efficient search methods and code-book modifications
G.728 low delay CELP codec 16 kbit/sG.729 CS-ACELP codec 8 kbit/sG.723.1 ACELP 5.3 kbit/s
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Voice coding: summary
G.711 PCM
G.726 ADPCM
G.728 LD-CELP
G.729 CS-ACELP
G.723.1 MP-MLQ
G.723.1 ACELP
64
32
16
8
6.3
5.3
0.125
1
0.625
10
30
30
Codec Bit rate(kbit/s)
Framesize (ms)
0
0
0
5
7.5
5
Lookahead (ms)
1972
1990
1992-94
1995
1995
1996
Year
RPE-LTP (GSM) 13 20 01987
G.722 Subband ADPCM 48-64 0.125 1.51988
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